Before you point me to Google or serverfault search I want to tell you that I've searched a lot, did some "fixes". They didn't help.

I have ISPConfig 3 installed on Ubuntu 12.04 LTS Server The server has several domains and lets call the main domain: example.com. I have also demo.com

I have several emails on each domain.

The status of the email sent between the emails:

[email protected] -> [email protected] (Success)
[email protected] -> [email protected] (Failure)

The failure is with error:
postfix/pipe[31311]: 8E72ED058D: to=<[email protected]>, relay=dovecot, delay=0.1, delays=0.03/0/0/0.07, dsn=5.1.1, status=bounced (user unknown)

I saw the fix for removing the example.com from:
mydestination = localhost, localhost.localdomain in /etc/postfix/main.cf
It didn't help.

Also an important thing is that the example.com MX records are Google's. We are using Google Apps for this domain in order to use Gmail servers.

I think the problem is that the mail server is not looking for the MX records of the domain. It knows the domain is set on this server and it searches for the destination email on the local server, not on Google's servers.

For several days I'm really lost!
Thanks for your help in advance!